i have an assignment for tomorrow and i still have 2 exercises that i didn't know how to resolve them.
I will be more than grateful if someone could help me.
Let A be an nxn invertible matrix. Show that if A is in upper (lower) triangular form,then A-1 is also in upper(lower) triangular form
Suppose B is row equivalent to the nxn invertible matrix A.Show that B is invertible.
Thanks in advanced!
For the first question, you can try a proof by induction on the dimension.
For the second one, how would you translate the condition of row equivalence in terms of matrices?
By the way, welcome to Math Help Forum!
for the second part, if B is row equivalent to A,then B is obtained by multipying A by a finite number of elementary matrices,namely, B=E1E2...EkA.So B is invertible as product of invertible matrices.